mirror of
https://github.com/aicodix/dsp.git
synced 2026-04-27 22:35:45 +00:00
119 lines
3 KiB
C++
119 lines
3 KiB
C++
/*
|
|
Some spline algorithms
|
|
|
|
Copyright 2018 Ahmet Inan <inan@aicodix.de>
|
|
*/
|
|
|
|
#pragma once
|
|
|
|
namespace DSP {
|
|
|
|
template <int KNOTS, typename OTYPE, typename ITYPE>
|
|
class UniformNaturalCubicSpline
|
|
{
|
|
OTYPE A[KNOTS-1], B[KNOTS-1], C[KNOTS-1], D[KNOTS-1];
|
|
ITYPE x0, dx;
|
|
public:
|
|
UniformNaturalCubicSpline() = default;
|
|
UniformNaturalCubicSpline(OTYPE *y, ITYPE x0 = 0, ITYPE dx = 1, int STRIDE = 1) : x0(x0), dx(dx)
|
|
{
|
|
ITYPE u[KNOTS-1];
|
|
u[0] = ITYPE(0);
|
|
OTYPE z[KNOTS-1];
|
|
z[0] = ITYPE(0);
|
|
for (int i = 1; i < KNOTS - 1; ++i) {
|
|
ITYPE l = ITYPE(4) - u[i-1];
|
|
u[i] = ITYPE(1) / l;
|
|
z[i] = (ITYPE(3) * (y[(i+1)*STRIDE] - ITYPE(2) * y[i*STRIDE] + y[(i-1)*STRIDE]) - z[i-1]) / l;
|
|
}
|
|
OTYPE c(ITYPE(0));
|
|
for (int i = KNOTS - 2; i >= 0; --i) {
|
|
A[i] = y[i * STRIDE];
|
|
C[i] = z[i] - u[i] * c;
|
|
B[i] = y[(i+1)*STRIDE] - y[i*STRIDE] - (c + ITYPE(2) * C[i]) / ITYPE(3);
|
|
D[i] = (c - C[i]) / ITYPE(3);
|
|
c = C[i];
|
|
}
|
|
}
|
|
OTYPE operator () (ITYPE x)
|
|
{
|
|
ITYPE tx = (x - x0) / dx;
|
|
int k = tx;
|
|
ITYPE t = tx - ITYPE(k);
|
|
if (k < 0) {
|
|
t = tx;
|
|
k = 0;
|
|
}
|
|
if (k >= KNOTS - 1) {
|
|
t = tx - ITYPE(KNOTS-2);
|
|
k = KNOTS-2;
|
|
}
|
|
return A[k] + t * (B[k] + t * (C[k] + t * D[k]));
|
|
}
|
|
};
|
|
|
|
template <typename TYPE>
|
|
struct CubicHermiteSpline
|
|
{
|
|
static constexpr TYPE h00(TYPE t)
|
|
{
|
|
return (TYPE(1) + TYPE(2) * t) * (TYPE(1) - t) * (TYPE(1) - t);
|
|
}
|
|
static constexpr TYPE h10(TYPE t)
|
|
{
|
|
return t * (TYPE(1) - t) * (TYPE(1) - t);
|
|
}
|
|
static constexpr TYPE h01(TYPE t)
|
|
{
|
|
return t * t * (TYPE(3) - TYPE(2) * t);
|
|
}
|
|
static constexpr TYPE h11(TYPE t)
|
|
{
|
|
return t * t * (t - TYPE(1));
|
|
}
|
|
static constexpr TYPE left(const TYPE *x, const TYPE *y)
|
|
{
|
|
return (y[0] - y[-1]) / (x[0] - x[-1]);
|
|
}
|
|
static constexpr TYPE right(const TYPE *x, const TYPE *y)
|
|
{
|
|
return (y[1] - y[0]) / (x[1] - x[0]);
|
|
}
|
|
static constexpr TYPE central(const TYPE *x, const TYPE *y)
|
|
{
|
|
return TYPE(0.5) * (left(x, y) + right(x, y));
|
|
}
|
|
static constexpr TYPE eval(const TYPE *x, const TYPE *y, TYPE t, int k, int n)
|
|
{
|
|
return k < 1 ?
|
|
h00(t) * y[0] + h10(t) * (x[1]-x[0]) * right(x, y) + h01(t) * y[1] + h11(t) * (x[1]-x[0]) * central(x+1, y+1)
|
|
: k < n-2 ?
|
|
h00(t) * y[k] + h10(t) * (x[k+1]-x[k]) * central(x+k, y+k) + h01(t) * y[k+1] + h11(t) * (x[k+1]-x[k]) * central(x+k+1, y+k+1)
|
|
:
|
|
h00(t) * y[n-2] + h10(t) * (x[n-1]-x[n-2]) * central(x+n-2, y+n-2) + h01(t) * y[n-1] + h11(t) * (x[n-1]-x[n-2]) * left(x+n-1, y+n-1);
|
|
}
|
|
static constexpr TYPE left(const TYPE *y)
|
|
{
|
|
return y[0] - y[-1];
|
|
}
|
|
static constexpr TYPE right(const TYPE *y)
|
|
{
|
|
return y[1] - y[0];
|
|
}
|
|
static constexpr TYPE central(const TYPE *y)
|
|
{
|
|
return TYPE(0.5) * (y[1] - y[-1]);
|
|
}
|
|
static constexpr TYPE eval(const TYPE *y, TYPE t, int k, int n)
|
|
{
|
|
return k < 1 ?
|
|
h00(t) * y[0] + h10(t) * right(y) + h01(t) * y[1] + h11(t) * central(y+1)
|
|
: k < n-2 ?
|
|
h00(t) * y[k] + h10(t) * central(y+k) + h01(t) * y[k+1] + h11(t) * central(y+k+1)
|
|
:
|
|
h00(t) * y[n-2] + h10(t) * central(y+n-2) + h01(t) * y[n-1] + h11(t) * left(y+n-1);
|
|
}
|
|
};
|
|
|
|
}
|
|
|